As is standard for Classical/Romantic-era concertos, the work is in three movements:

Allegro con brio. This movement is known to make forceful use of the theme (direct and indirect) throughout.

Orchestral exposition: In the orchestral exposition, the theme is introduced by the strings, and used throughout the movement. It is developed several times. In the third section (second subject), the clarinet and violin 1 introduce the second main theme, which is in the relative major key, E-flat major.

Second exposition: The piano enters with an ascending scale motif. The structure of the exposition in the piano solo is similar to that of the orchestral exposition.

Development: The piano enters, playing similar scales used in the beginning of the second exposition, this time in D major rather than C minor. The music is generally quiet.

Recapitulation: The orchestra restates the theme in fortissimo, with the wind instruments responding by building up a minor ninth chord as in the exposition. For the return of the second subject, Beethoven modulates to the tonic major, C major. A dark transition to the cadenza occurs, immediately switching from C major to C minor.

Cadenza: Beethoven wrote one cadenza for this movement. The cadenza Beethoven wrote is at times stormy and ends on a series of trills that calm down to pianissimo. Many other composers and pianists have written alternative cadenzas.

Coda: Beethoven subverts the expectation of a return to the tonic at the end of the cadenza by prolonging the final trill and eventually arriving on a dominant seventh. The piano plays a series of arpeggios before the music settles into the home key of C minor. Then the music intensifies before a full tutti occurs, followed by the piano playing descending arpeggios, the ascending scale from the second exposition, and finally a resolute ending on C.

Largo. The second movement is in the key of E major, in this context a key relatively remote from the concerto’s opening key of C minor (another example being Brahms’s first symphony.). If the movement adhered to traditional form, its key would be E-flat major (the relative key) or A-flat major (the submediant key). The movement opens with the solo piano and the opening is marked with detailed pedalling instructions.

Rondo. Allegro. The finale is in sonata rondo form. The movement begins in C minor with an agitated theme played only by the piano. The movement ends with a C major coda marked presto.

Beethoven composed this work in 1799-1800, and introduced it at Vienna on April 5, 1803. The first sketches go back to 1797 – after he’d composed the B flat Piano Concerto (published as No. 2), but before composition of the C major Concerto (in 1798, published as No. 1). Although Beethoven played the first performance of No. 3 in 1803 from a short score – no one was going to steal it from him! – he’d actually completed the music prior to April 1800, apart from a few last-minute adjustments. In other words, before he wrote the Second Symphony (Op. 36), the Moonlight Piano Sonata (Op. 27/2), or the Op. 31 triptych for keyboard.